The Minister for Education and Science, Mr Dempsey, has expressed his confidence that the enrolment crisis in Limerick schools will be resolved later this week.
This follows a series of specially-convened meetings yesterday with local politicians, officials from his Department, and representatives from schools in the areas to discuss allegations that some schools were operating a policy of "educational apartheid".
Seventeen students in the Limerick city area, mainly from disadvantaged areas, are currently without a place at second level.
But in a significant development, principals from second-level schools in the city have agreed to meet again on Thursday to discuss how to facilitate those students who want to continue their second-level education.
It is understood that up to 12 of the 17 Limerick boys who had been denied places in Limerick secondary schools want to resume their education.
The new agreement means any student still without a second-level school should be able to find a place at a school in the area, with priority given to children from schools in Limerick city.
In the meantime, talks are due to continue with the National Welfare Education Board and the Department of Education over the remainder of the students, some of whom are understood to want an alternative to secondary school education.
Speaking to The Irish Times after nearly six hours of meetings, Mr Dempsey said the meetings had been "very positive". However, although agreement has been reached to resolve the immediate difficulties, work remained to be done to ensure the issue did not arise again. It is understood the Department of Education made it clear from the outset of the meeting that were the issue not to be resolved at the meeting, then Mr Dempsey was prepared to put regulations in place to compel schools to take in certain children.
One source present at the meeting said there was some "fairly tough talking" from both sides. But the general feeling was that everyone present wished to see the issue resolved.
"I am confident from what I heard today that of those students that want to attend mainstream school that they will be facilitated, and that will be worked out on Thursday," Mr Dempsey said.
Ahead of yesterday's crisis talks, the Minister said he was "appalled" at the situation in Limerick, and he warned that schools could not exclude pupils from certain areas of the city.
Under the Education Act, schools can introduce admission policies, but are not allowed to discriminate on grounds such as exam results or students' social backgrounds.
Following yesterday's meeting Mr Dempsey also reiterated his stance that the school places problem in Limerick was not about a question of resources.
"I think if you got the addresses of all of the students that were excluded you would find a remarkable similarity, and the areas from which the students were refused would be well known to people in Limerick. It seems to be happening only to boys, and there's no similar problem among girls," he said.
Mr Dempsey also said that certain principles had been agreed in relation to future admissions procedures in Limerick.